$#C+1 = 50 : ~/encyclopedia/old_files/data/S087/S.0807200 Star body
An open set $ \mathfrak S $
3 KB (521 words) - 20:42, 16 January 2024
Two functions $ K ( x, s) $
and $ K _ {1} ( x, s) $
3 KB (440 words) - 17:48, 13 January 2024
...p in the ring of all endomorphisms of this group is a division ring (Schur's lemma).
587 bytes (95 words) - 19:54, 11 April 2014
\int\limits _ \Omega K ( x , s , \phi ( s) ) d s + f ( x) ,\ \
...bounded closed set in a finite-dimensional Euclidean space and $ K ( x , s , t ) $
3 KB (455 words) - 08:27, 6 June 2020
...tioned into left ideals which are (necessarily isomorphic) groups; and d) $S$ is the direct product of a group and a right zero semi-group (cf. [[Idempo
1 KB (167 words) - 17:09, 8 January 2021
...{a_s\}$ and $\{b_s\}$ be certain sets of complex numbers, $s\in S$, where $S$ is a finite or an infinite set of indices. The following inequality of Hö
...q \Bigl(\sum\limits_{s\in S}|a_s|^p\Bigr)^{\frac1p}\Bigl(\sum\limits_{s\in S}|b_s|^q\Bigr)^{\frac1q},
4 KB (729 words) - 16:13, 29 November 2012
If $ \mathbf r = \mathbf r ( s) $(
where $ s $
3 KB (450 words) - 19:38, 5 June 2020
L(a,s) = \sum_{n=1}^\infty a(n) n^{-s}
L(a,s) + L(b,s) = \sum_{n=1}^\infty (a+b)(n) n^{-s}
2 KB (358 words) - 17:25, 11 November 2023
A function $(x,s)\mapsto K_n(x,s)$ that is formed from the given kernel $K$ of an [[Integral operator|integr
$$K_1(x,s)=K(x,s),\quad K_n(x,s)=\int\limits_a^bK_{n-1}(x,t)K(t,s)dt.$$
2 KB (292 words) - 19:24, 9 October 2014
...phere]]. This group is presented by generators $R$, $S$ and relations $R^3=S^3=(RS)^2$.
* {{Ref|a1}} H.S.M. Coxeter, "Regular complex polytopes", Cambridge Univ. Press (1991) pp. 7
365 bytes (50 words) - 13:54, 8 April 2023
...ally assumed that the effect of the noise on the signal is additive: $x(t)=s(t)+n(t)$. In such a situation the problems of signal extraction are as outl
...More involved varieties of the initial hypothesis are also studied: $x(t)=s(t)+n(t)$ starting from some moment, possibly random, of time $\tau$, which
2 KB (383 words) - 14:54, 13 August 2014
...ring of fractions (cf. [[Fractions, ring of|Fractions, ring of]]) $ A [ S ^ {-1} ] $,
where $ S $
4 KB (713 words) - 21:35, 4 January 2021
''of a convex surface $S$''
...ting from some point $O\in S$ and belonging to the convex body bounded by $S$. The limit cone is defined uniquely, up to a parallel displacement dependi
1 KB (161 words) - 05:57, 18 October 2014
defined by G.W. Whitehead. In $ S ^ {k} $
Then the product of spheres $ S ^ {m} \times S ^ {n} $
4 KB (505 words) - 15:48, 29 March 2021
...$ is introduced on the bicharacteristic strip, then its equations $x_i=x_i(s)$, $i=1,\dots,n$, are defined by solving a system of $2n$ ordinary differen
\begin{equation}\dot x_i(s)=Q_{\xi_i},\quad\dot\xi_i=-Q_{x_i},\quad i=1,\dots,n.\label{*}\end{equation
3 KB (419 words) - 22:32, 10 December 2018
with at most a countable set of states $ S $:
i, j \in S.
2 KB (239 words) - 09:50, 29 October 2023
A morphism of schemes $ f: X \rightarrow S $
such that the pre-image of any open affine subscheme in $ S $
3 KB (464 words) - 05:59, 19 March 2022
U = \alpha _ {1} X _ {1} + \dots + \alpha _ {s} X _ {s} ,\ \
V = \beta _ {1} X _ {s+1} + \dots + \beta _ {t} X _ {s+t} $$
3 KB (346 words) - 08:00, 25 April 2022
A model of the manifold of lines in a three-dimensional elliptic space $ S _ {3} $
on a pair of two-dimensional elliptic planes $ S _ {2} $.
3 KB (461 words) - 19:40, 5 June 2020
...$. The shortest-path problem is to find a least cost (shortest) path from $s$ to every other vertex (node) $i$.
...eeds by constructing, one node at a time, a subtree $T$ rooted at $s$ (an $s$-[[arborescence]]). If $\Gamma$ is connected, $T$ will be a spanning subtre
2 KB (405 words) - 19:42, 6 September 2017